This answer to your question is subjective, but I'd consider 60% identity quite high, especially if the domain structure of your protein is not altered from its closest analogous sequence. I'd recommend you do not change the name. This will help researchers locate your publications more easily and ultimately may lead to a higher number of citations. However, if your protein has an alternate function than the function of the closest analogous protein, then it may be prudent to consider an alternative name to distinguish as such.
Whether you give the new protein a different name depends on the function of the protein and whether the name reflects a general or specific function. Some enzymes can have very different activities with a few amino acid differences. The cytochrome P450s are a great example of defining families and subfamilies by % identity but the point is within each grouping, the constituent enzymes can still have very different functions.
As Markus already told you, is preferable to name your protein according to its function (or apparent function). For me, a 60% identity value is quite high. What about the similarity value? it is surely higher than 60% and it could be more informative.
I'm interested in the conserved aminoacids. If you know what the function of your protein is or what the function of the closest relatives is, and if the conserved aminoacids are involved in catalyzing the enzymatic reaction, then you should consider to not rename the protein as the protein has *probably* the same function than your closest sequence.
It could be useful to know what's the source of your protein (plant, virus, bacteria...) and if the database you're using to run the blast has a wide coverage of related organisms.
The last thing I'd like to suggest, is to analyze the structure of the protein. There are servers to predict the tertiary structure (one of my favorites is the I-tasser, by the Yang Zhang lab, but there are others). This will tell you if your protein can fold in the same -or nearly the same- structure than the closest protein and therefore if their functions are related.
As the final note: by all means, try to not give the protein a new name, unless of course it is absolutely necessary. Our protein naming system is, actually, a mess. We all sigh when trying to find a protein that has been named by around 10 000 groups over the world.
thanks at all! ok, my putative protein is like xanthorhodopsin (the identity was 45%, I made a mistake). Bacteriorhodopsin, archeorhodopsin, proteorhodopsin (PR) and xantorhodopsin (XR) have the same function. between PR and XR there is a 33% identity and the same aa conserved for the function. As in proteorhodopsin and xantorhodopsin, the internal proton donor is Glu. Seven transmembrane alpha helices, conserved AA residues necessary for the function suggested that my sequence likely encoded a retinal-binding ion transporters that can create a proton electrochemical potential. So, I will call putative xantorhodopsin to my sequence. Thanks!